In most cases your auto insurance provider will pay you for the actual cash value of your vehicle. Actual cash value equates to the replacement cost of your vehicle minus depreciation.
If you have comprehensive & collision coverage (comp and collision), your insurance company will write you a check for actual cash value, less your deductible.
If you owe more on your loan or lease than your vehicle is worth, then you should consider GAP insurance. Without GAP insurance, you will be responsible for any remaining balance on your loan.
The best way to save money on car insurance is to shop around for the cheapest rate.